Triply Periodic Minimal Surfaces - Batwing Family

Schoen's Batwing Surface

The left image shows two fundamental regions, whose appearance is the
source of the name "batwing". The two fit in a tetrahedron, which is
1/48 of a full lattice cell cube. The second image shows 12 fundamental
regions in a cube. This appears to the eye to be a lattice fundamental
cell, but it is not. Opposite edges almost match under translation,
but there are actually gaps of about .02.
The third image is the full cubical unit cell.
The fourth image shows the surface as a chamber with tubes
in a slightly flattened octahedron. The genus of this surface is 25.
Evolver file: batwingadj.feBuy from Shapeways.com (unit cell)
Buy from Shapeways.com
(1/8 unit cell)

Brakke's Pseudo-Batwing Surface

This is the surface suggested by the near-symmetry of the small batwing cube.
The left image shows a full lattice fundamental cell. The difference from
the corresponding batwing piece is the cube face mirror symmetry planes are
replaced by C2 axes on the cube face diagonals. The middle image shows two
pseudo-batwing cells, and the right image shows the corresponding two
batwing cubes, for easy comparison.
Evolver file: pbatadj.feBuy from Shapeways.com
(1/8 unit cell)

Schoen's Batwing-41 Surface

This is a higher genus version of the Batwing surface, with genus 41.
The left image shows two fundamental regions, whose appearance is the
source of the name "batwing". The middle image shows 12 fundamental
regions in a cube.
The third image is the full cubical unit cell.
The fourth image shows the surface as a chamber with tubes
in a slightly flattened octahedron.
Evolver file: batwing41adj.fe

Schoen's Batwing-57 Surface

This is a higher genus version of the Batwing surface, with genus 57.
The left image shows two fundamental regions, whose appearance is the
source of the name "batwing". The middle image shows 12 fundamental
regions in a cube.
The third image is the full cubical unit cell.
The fourth image shows the surface as a chamber with tubes
in a slightly flattened octahedron.
Evolver file: batwing57adj.fe
Back to
Triply Periodic Minimal Surfaces.
Back to
Ken Brakke's home page.